The angular impulse-momentum relation


Angular momentum of a particle: The symbol HO denotes the angular momentum and is defined as the moment of linear momentum around the point O, and given by the equation




Example 1

Example 2


Impulse of a moment from time t1 to t2: The integral of the moment over the time interval of concern is its impulse. The impulse of a moment is a vector given by the integral



Moment and rate-of-change-of angular momentum relation: Starting from Newton’s second law, calculating the moment of both sided of the equation with respect to a point O on an inertial frame results in



This resulting relation between the moment and the rate of change of angular momentum is called the moment-rate of change of angular momentum relation (MRCAM).


Example 3


The angular impulse-momentum relation: Integration of Newton’s 2nd law over the time interval from t1 to t2 results in

Therefore, the angular momentum of a particle is changed by the impulse of the resultant moment on the particle. There will be conservation of angular momentum only if the impulse of the resultant moment is zero.


Example 4



ã Mehrdad Negahban and the University of Nebraska, 1996-2002.

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Department of Engineering Mechanics, University of Nebraska, Lincoln, NE 68588-0526